Cremona's table of elliptic curves

3034 = 2 · 37 · 41

Field	Data	Notes
Atkin-Lehner	2+ 37- 41+	Signs for the Atkin-Lehner involutions
Class	3034a	Isogeny class
Conductor	3034	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-10445115392 = -1 · 212 · 37 · 413	Discriminant
Eigenvalues	2+  1  0 -4 -3 -1 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1216,-17138]	[a1,a2,a3,a4,a6]
j	-198614491413625/10445115392	j-invariant
L	0.80608723925944	L(r)(E,1)/r!
Ω	0.40304361962972	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24272e2 97088c2 27306j2 75850i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3034a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	1	0	-4	-3	-1	-3	2	3	6	8	-	+	-1	-3	0	15	8	-13	0	11	-4	6	9	2

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Quadratic twists for elliptic curve 3034a2

-4	8	-3	5	37	41
24272e2	97088c2	27306j2	75850i2	112258c2	124394a2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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